Iran and the P5+1 group -- the United States, Russia, China, France, Britain and Germany -- effectively gave themselves until Friday to agree a deal by extending the terms of a 2013 interim accord under which Iran has been curtailing its nuclear programme in return for sanctions relief.
"Removing the remaining brackets (in the text of the agreement), this seems to be very, very, very tough," the senior diplomat said as an 11th day of talks stretched late into the night in Vienna.
This was rammed home by a second diplomat, who said the new target date -- the latest in a string of postponements in almost two years of talks seeking to end a 13-year standoff -- is the "final" one.
"It's difficult to see why and how we could go on any longer. Either this works in the next 48 hours or it doesn't," the second diplomat said on condition of anonymity.
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"We have never been closer, than we've ever been on this agreement, and we are still not where we need to be to finalise a deal," a senior US administration official said.
Their Russian, Chinese, French and British counterparts had already left. The latter two said they would return to the Austrian capital tomorrow evening.
"If very tough political decisions, hard choices, can get made soon, I do believe we can get to an agreement ... It is possible," the US official said.
For many observers July 9 had always been the real deadline, and the US team now has its back against the wall trying to nail down the final details by then.
If Kerry fails to hand over a deal by the end of Thursday, US lawmakers will get 60 days instead of 30 to review it, which risks further complicating its implementation.
In return sanctions on Iran would be progressively lifted.
Despite progress on a series of complicated annexes, talks have stalled on how to ease sanctions against Iran, probing allegations that in the past Tehran sought to develop nuclear arms, and ensuring Iran can continue to have a modest, peaceful nuclear programme.
Russian Foreign Minister Sergei Lavrov confirmed there was disagreement over the issue of lifting of a UN conventional also arms embargo which bans sales of convention weapons such as tanks and missiles to Tehran.